THE ELEATICS

Around 535 BC, a group of Greek settlers founded a colony on the west coast of Italy, just south of the modern city of Napoli (Naples). The settlement eventually became known as Elea.

On its own, Elea was unremarkable and would be a footnote in history (or more aptly, archeology) but for one small detail – it is the birthplace of Western philosophy!

Elea is known almost exclusively for two of its citizens: Parmenides, the father of Western philosophy, and Zeno, his much more famous student and apologist; together with Melissus of Samos (and possibly Xenophanes), they constitute the entire Eleatic School of Philosophy…at least until certain 20th century thinkers picked up their mantle.

Reluctant students of philosophy will be amused to learn that Eleatic philosophy is, to say the least, enigmatic. Some might call it indecipherable. I can almost hear the adolescent chants in the halls of the Philosophy Department: “Nonsense then, nonsense now.” Whether that is true or not, I will leave to the reader of this essay.

Let’s start with Parmenides, the granddaddy of them all. Born 515 BC, he left us a great ontological poem, On Nature. Unfortunately, only fragments of the poem survive and scholars disagree: if we had the entire text, would its meaning be clearer, or would it still confound us? (I suspect the later.)

After a brief Prologue, Parmenides divides the body of the poem into two sections; each presents a particular vision of reality (or being): Aletheia (The Way of Truth) and Doxa (The Way of Appearance or Seeming). The two models have almost nothing in common.

Over the past 2,500 years, philosophers from Plato on have attempted to “explain” Parmenides’ meaning. It is far from clear that anyone has got it right; and if someone has, that interpretation has not inspired consensus. Each new generation of would-be philosophers sets out anew to crack Parmenides’ code.

The key to the problem would seem to be our understanding of the ‘Truth/Appearance’ dichotomy. Further, the real problem seems to lie with our understanding of the 2nd term of this dichotomy, Doxa. Here are some of the solutions floated:

(1) Aletheia is “truth”, so Doxa must be “falsehood, deception (or) delusion”.

(2) Aletheia is “being”, so Doxa must be “maya” (as in Eastern spirituality).

(3) Aletheia corresponds to the world of Platonic Ideas or Forms while Doxa corresponds to the shadows projected on the wall of Plato’s cave.

(6) Aletheia is the world seen under the aspect of ‘eternity’ while Doxa is that same world seen under the aspect of ‘extension’ (i.e. spacetime).

(7) Doxa is the world with events ordered according to the 2nd Law of Thermodynamics (entropy) and the principle of causality. Aletheia is the mirror image of that world; events are negentropic and ordered according to the principle of teleology.

Doubtless there are other potential solutions as well. However, with the conspicuous exception of #1, these options require Parmenides to have an independent understanding of concepts that did not enter the mainstream of Western philosophy until much later. Not impossible, but a stretch!

Perhaps worse, there is nothing probative in Parmenides’ own words that might lead a reader to choose with confidence one of these interpretations over all the others. As a result, Eleatic Philosophy has been a kind of Rorschach test: later philosophers project their own philosophical conclusions onto the Eleatic canvass.

But now it’s time to let On Nature speak for itself. Re Aletheia:

“What-is is ungenerated and imperishable, whole, single-limbed, steadfast and complete. Nor was it once, nor will it be, since it is, now, all together, one, continuous…whence did it grow? Not from what is not…It must be completely, or not at all.

“How could what-is be in the future; and how could it come to be? For if it came to be, it is not, nor is it if at some time it is going not to be. Thus, coming to be is extinguished and perishing not to be heard of.

“Nor is it divisible since it all alike is…it is full of what is.

“It is not right for what is to be incomplete…it is not lacking; but if it were, it would lack everything.”

While re Doxa:

“It has been named all things that mortals have established, trusting them to be true: to come to be and to perish, to be and not to be, to shift place and to exchange bright color.

“And they distinguished opposites in body and established signs apart from one another…Everywhere the same as itself but not the same as the other.

“Thus, according to belief, these things were born and now are, and hereafter, having grown from this, they will come to an end. And for each of these did men establish a distinctive name.”

Perhaps we can get a clue to the meaning of On Nature by studying the better known work of Parmenides’ student, Zeno. From what we know, Zeno was devoted to Parmenides and determined to defend his views against all comers.

Doxa presents what modern day intellectuals might call a ‘common sense’ view of the world. WYSIWYG: what you see is what you get! In philosophical terms, a proponent of the Doxa world view might be called a ‘rationalist’, an ‘empiricist’, a ‘pragmatist’, a ‘realist’ or even a ‘naïve realist’.

If On Nature argues, as it almost certainly does, that the world cannot be understood in terms of Doxa, or at least not solely in terms of Doxa, then it is a frontal assault on the ‘common sense’ view of the world.

It requires us to admit that ‘common sense’ is neither as ‘common’ nor as ‘sensible’ as we had imagined. Either we discard Doxa entirely or somehow combine Doxa with Aletheia to produce a comprehensive and self-consistent model of reality.

Obviously, such teaching would inflame passions and perhaps subject Parmenides to the derision of the crowd. In my own lifetime, I can recall philosophers being referred to as ‘egg heads’. A common joke went like this: British philosophers say they don’t believe in causality; but on a cloudy morning, not one of them leaves the house without an umbrella.

We know from Aristophanes (The Cloud), that 5th century BC Athenians were also only too eager to make fun of their philosophers, especially Socrates.

It must have pained the starry-eyed Zeno greatly to see his mentor ridiculed in the marketplace. Zeno made it his life’s work to defend Parmenides against all such attacks. But how?

Zeno knew that defending Parmenides line by line was a fool’s game. Like Whack-a-Mole, win one argument and another one pops right up!

So Zeno took a different route. He channeled his teaching into a series of ‘paradoxes’. Ingeniously, Zeno designed his paradoxes, not just to prove Parmenides’ detractors wrong in one instance, but to prove that no ‘common sense’ (WYSIWYG) model of the reality can ever be right. According to Zeno, Parmenides is right, not accidentally but necessarily!

Take that, you naïve realists!

Reader, you may now exhale. I do not intend to spell out each of Zeno’s paradoxes. You’re probably already familiar with the broad outline of at least some of them; if not, there are libraries full of essays spelling out the details of each.

I will quickly outline one such paradox and then move on: Achilles, the fastest runner in all of Greece, is challenged to a race by, of all creatures, a Tortoise. Achilles accepts, but being a sporting individual, he gives the Tortoise a head start.

Achilles starts at T-1 while the Tortoise starts further along the course at T-2. For Achilles to overtake the Tortoise, he must first get to T-2, the Tortoise’s starting point. But by the time Achilles gets to T-2, the Tortoise has advanced to T-3. Now Achilles must get to T-3; but by the time he gets to T-3, the Tortoise has advanced to T-4, and so on ad infinitum. Bottom line: Achilles can never catch the Tortoise.

Commentators on Zeno have seriously debated whether Zeno actually believed that Achilles could not catch up to the Tortoise. Really? Of course, Zeno knew that the Achilles in our midst crush us Tortoises every day of the week. In fact, quite literally ‘everyone’ knows that Achilles wins the race; and Zeno’s paradox depends on just that!

You see, the problem is not that Achilles cannot catch the Tortoise. The problem is that Achilles does catch the Tortoise…but there is no way to account for that that is consistent with the ‘common sense’ principles of space, time, motion and arithmetic.

Zeno, and no doubt Parmenides before him, believed that the ‘common sense’ model of the world (Doxa) was hopelessly inconsistent with the ‘common sense’ precepts of logic, mathematics and physics. In other words, like Wittgenstein (below), Zeno did not believe that the phenomenal world could give a comprehensive and consistent account of itself.

So what! Well, if Doxa cannot give a complete and consistent account of itself, then either (1) we concede that the world is ‘absurd’ (Nietzsche, Camus, Ionesco, et al.) or (2) we need to appeal to something transcendent, something beyond Doxa, something like Parmenides’ Aletheia.

Was Zeno successful? Is the reasoning of the paradoxes valid? Well, just as On Nature has confounded philosophers for millennia, so have Zeno’s paradoxes. Each new generation of philosophers claims to have solved (i.e. debunked) them; each succeeding generation rejects those so-called ‘solutions’ and reasserts the validity of the paradoxes themselves.

The physical, logical and mathematical validity of Zeno’s arguments is still debated today. A book published in the late 20th century (Zeno’s Paradoxes) consists of 11 essays, spanning the most recent 100 years; the essays go back and forth on the validity of Zeno’s arguments.

So, what do I think? Do I think the reasoning of the paradoxes is valid? I neither know nor care!

Of course, I do care – deeply in fact, or I wouldn’t be writing this essay, would I? But I lack the formal training (and talent) in logic and mathematics necessary to make an original contribution to the debate. Like most other would-be philosophers, I would merely be projecting my own views onto the Eleatic canvass (above).

Fortunately, however, Zeno’s underlying hypothesis about the world, if not the validity of his arguments, has been settled once and for all by other thinkers using other means. In fact, the intellectual history of the 20th century is the story of naïve realism’s ultimate defeat. It is no longer reasonable to assert that real world events can be explained by the principles of Doxa.

These modern thinkers not only endorsed Zeno’s fundamental hypothesis re the world; they also followed his method. They were not content to demonstrate anomalies in the WYSIWYG model; in each case, they proved that WYSIWYG is the anomaly and that no such special case is possible!

Schrödinger, Heisenberg, Gödel, and Bell have rendered Zeno irrelevant (outside of intellectual circles), but they did so while standing on his shoulders (and therefore on the shoulders of Parmenides too). One might even say that Zeno was the 20th century’s first philosopher!